Bags of Holding and N dimensions

[nitouken]

According to Ephemeralstability

Although the following argument is for finitely many dimensions, it can be extended to countable or even uncountable-dimensional vector spaces.

Consider a bag of holding of dimension n. It can contain a vector space A of dimension at most n. Suppose it can contain other bags of holding. Then take the power set of A (i.e. set of all subsets of A). This can be represented as a set of bags of holding all containing subsets of A. There must be 2^n dimensions to contain all these bags and therefore the dimension of the bag of holding would be greater than n which is a contradiction. Therefore the bag cannot contain other bags.

I just read the "Golems are fantasy robots" thread, and this caught my eye. I wanted to see if anyone else had something to add.
This is a proposal that some GMs may allow, maybe not, but it is an argument for why bags of holding should be allowed into each other.
If you are considering the bag of holding to be of dimension X, then you overlook one important fact. In bag A, you have a given area, X. Bag B, physically, can be assumed to have an external area, Z, which is <X, right? We then define the internal area of bag B to be Y. Since we are assuming that the two bags are of equal size and open in to a non coplanar vector space, then the area defined by X after you put bag B into bag A is not in fact X^2, but X-Z. It is the internal area of bag B that is important. Thus the total capacity of the two bags is X+Y-Z. However, if bags of holding are assumed open into coplanar spaces, then this entire argument is moot. However, you have an entirely new option open to you.

If bags of holding open into coplanar spaces, then no bag could be placed into another, safely. However, they all open into the same plane. A well provisioned party would be able to travel from bag to bag. Call this plane Bag-plane. Traveling on bag-plane could be hazardous, but what if you have a spell like intuit direction? Then you can find your way from bag to bag, and eventually create a map of the bag-plane. This could be an entire world of adventures, as adventurers get the bright idea of either A: Looting other peoples' bags of holding, or B: building an easy access stronghold on the bag-plane, with portals leading to and from bags placed on the Material Plane for very quick access anywhere, but without the telltale magical signature of a portal.

Credits for this idea go to Kenzer and Co. Don't sue me, please.

Okay, I realize that in most campaigns, a bag of holding has a finite amount of space in it, and I think that is perfectly fine. However, then, unless you come up with some reason otherwise (Hint: magical fields), there is no good reason why one bag of holding could not contain another.

And, yes, I realize that many terms and descriptions were D&D. I apologize, I just think they are the best way to describe what I am trying to say. You should be able to translate fairly easily.

Edit: On rereading ephe's post, I see what she was saying, and why it could be valid. However, I still stand by my argument. No offense, ephe.

[Agar]

Okaaaaay. Someone was able to stay awake through calculus. I really only have a glimmer of what you're talking about. Sounds like you're trying to mathmatically prove or disprove if a bag of holding could hold another bag of holding.

My biggest question would be: Why would you want to?

You can carry more loot if you can put a stack of 8 ounce bags into a bag that can hold 50 pounds, but if they're going through that level of extreme pillaging, they need something better to do with their time, like a dracolich.

If there's some bizzare tax on magical items they're trying to avoid, they need to just suck it up and pay it. Misers.

I've always liked the idea of them exploding when placed inside each other for it's possibilites. What would make them sacrifice not one, but two of their most treasured items? Not something an adventurer would do just as a distraction. A desperate sacrifice to secure the safety of a greater good, a vicsious assassination of a vital target, those are possiblities.

So, not to disregard the validity of the arguments presented, I don't think the issue is of a big enough concern to use this much math on. If you have a player deserately trying to show you why, just say 'I'm the DM and that's how it works here.' and tell them to drop it.

I do like the Bag plane idea, but that doesn't require on bag inside of another to work, it just keeps them from taking bags with them.

[MoonHunter]

I think most of it is an issue of a) do all the bags empty to the same place and b) The more important of the two - What keeps the contents of each bag separate?

If no bagverse exists, then the extra space in each bag is simply a counter bulge in the local spacetime anchored to the bag's opening.  Put too many together, and the counter bulge gets bigger... eventually breaking and all the material would fall to the focus of the counter bulge (black hole, vertices, etc).  If no bagverse exists, then the contentents are maintained by the walls of the bag, which form the side of the counter bulge.  

If the Bagverse does exist and it vaguely resembles three dimensional space, then we have to ask what keeps all these things seperate?  My guess is that we have some intelligence with the ability to exert some "force" doing it.  Otherwise the conents of a bag could spill out of their pile and find their way into another pile.  

Insert anything from extradimensional gnomes/ gremlins, to demons, to avatars of order, to a small deity.  It could just come out into an automated warehouse in the 32nd century, where your explorers will get filed or recycled if not claimed in 30 days.  

Picture a vast cube of area, with a matrix of poles.  On these poles hang huge bags. Some spirit creature flys around making sure these bags are intact and possibly syphoning some energy off from those other planes to live...    Enter into a bag, cut the side and find yourself falling and spirit creatures fighting you to keep you inside.

[ephemeralstability]

I'm not entirely sure about the you worded your argument: when you say area do you mean the volume of n-space dispaced by the bag upon embedding? If so I agree, but I can't exactly see how coplanarity comes into it or indeed which spaces were supposed to be coplanar.

I wouldn't take it that seriously, though. At the time I was simply making something up on the spur of the moment. You could equally present a counterargument:

Since a bag of holding is simply a portal to another space it can be homotopically deformed to in R^3 to a point. Assuming the interior is a complete non-empty metric space without isolated points we can therefore embed uncountably many of these points in the interior of the bag, so we can fit infinitely many points inside.

I'm sure there are even more interesting arguments involving Banach-Tarksi-like decompositions of the interior.

The point is that in considering bags of holding you have to make assumptions about the way they embed and the way things embed in them. Those assumptions are not testable. For obvious reasons.

By the way, it's he not she!

ephe!

[nitouken]

My sincerest apologies. I think this post should be placed in the cavern of inane natter, rather than taken seriously. I was a little tired when I wrote it. Anyway, sorry, ephe, I thought I had seen someone refer to you as a woman.  

[ephemeralstability]

Only at weekends

[QUIM_B]

Have you thought of the implications of incorporating into the game the creator of the bags and thereby the bagverse? One could assume that the bags of holding, like many other spells and artifacts, were developed by some powerful wiz-mage through a process of experimentation. it could be that the creator sells these bags to merchants and adventurers as simply a teleportation spell to some dusty closet in his or her castle-keep, thus giving the wizard unlimited access to other people's stuff. How many gamers keep that careful track of every little thing they drop into the bag? How often have your characters gone to pull out that +3 battleaxe that you stole from the Orc King to find it mysteriously less powerful, or simply not there? Once again it all comes down to how involved in the details the players and GM want to get.

[Aidan]

What if the bag is turned inside out?

[Siren no Orakio]

One of a few things happen: Either very, very bad things that we just don't ever want to have to think about, ever. The prime material plane and the bag-verse switch places in one, horribly nauseating twang. The rules of reality go haywire, and all creation explodes.

Or... the bag rips, explodes, someone takes many, many, many d6 of damage.

Or... Nothing. Absolutely nothing. The bag continues to function as normal, the new inside indistinguish table from the first one.

[Kassil]

Or... We get a dimensional vortex and the character who did it finds himself wedged inside the extradimensional space, with the bag in there with him. Try getting outta that one...

[Ylorea]

What if the bag is turned inside out?

Well think about this thing... I can stick any normal polearm and even a huge polearm into a bag of holding.
(At least in my world you can. I normaly only keep track of the weight limit, as long as people do not stick in sharp objects. Just to be on the safe side, I assume the head of the polearm to be wrapped in cloth.)

The polearm will sort of not "touch" the side of the bag of holding, so if you reach inside to grab the side of the bag to pull it inside out, you are going to have a darn hard time....

to get back to the original thema of this post. I stick with the normal D&D rule.. Puttin one extradimensional space into another is simply impossible. A explosion is the result. Mathematicaly speeking, I see a bag of holding as a rupture in our standard four dimensional space to a other n-dimensional space.
The problem does not occur because one n-dimensional space could not potentialy exist in another m-dimensional space (even if n is greater then m), but forcing the rupture that connects our space to the first bag of holing thru a rupture that connects our space to the second bag of holding would cause the explosion.
(You essentialy need to disconnect the first extradimensional space from our dimension and then reattach it to another dimension. This is next to impossible)

Yours,

Ylorea

p.s. I love the idea of the teleportation bag of holding. (Think of the possiblity if the closet would get stolen by a thieves guild.... *evil grin*)

[KTheorem]

Not to nit-pick but if you are talking about D&D Bags of Holding then none of this applies.

A bag of holding's inside is non-dimensional space. It isn't a part of any plane whatsoever. The inner volume of a bag of holding is greater than it's outer volume. It's weight is constant because everything in it does not reside on any plane (including the one you are on).

There is nothing to suggest putting one bag of holding into another would do anything untoward. The outside of a bag of holding is innocuous and the inside is non-existent.

Turning a bag of holding inside out simply dumps out everything in it. And anything sharp in it could rip a hole in the bag from the inside causing the contents to spill out.

It seems that the closest object in D&D you are describing would be a Portable Hole which uses an extra-dimensional space to access a non-dimensional space (based on the effects of combining holes and bags, as well as the fact that it is often used for such purposes, I would say the extradimensional gate goes through the astral plane). Portable holes and bags of holding react badly with each other. When the bag is placed into the hole they both go to the astral plane. When a hole is placed in a bag, both are destroyed and everything within 10 ft goes to the astral plane. Portable holes aren't mentioned as being dangerous to stack together.

[Pariah]

I think what they're trying to get at is how, in a rational, functioning universe, does a bag of holding do its job.  If it put the stuff into a non-existent space, being one where nothing exists, it would defy one of the basic laws of sanity.  Matter cannot be created or destroyed only transformed, and Matter must have mass and volume.

Even the dnd universe would be a rational, functioning universe, except when the gods have absolute power, being that the dnd pantheon doesn't have this and are still mostly tied down by basic laws like that.  I can say that because wizards STUDY magic, it isn't some innate gift in many of them, they have no real power over mos things, and everything they do can be explained, pretty convincingly, with a couple of minutes of thought.

Now on to the question at hand, "what would happen if you turned the bag inside out?"  I personally think that if it is connected to the bag-verse then the god thingy of the bag-verse wil smite you repeatedly until you are dead, otherwise a lot of d6's of damage seems reasonable, if not a little light.  I think that it would be better if you dealt them the same number of dice but change the d6 to a d100.  But thats just me.

Or an even funner idea would be that it immediatly causes the death of magic, which would be REALLY funny.  the party's arch-mage is worse then is useless and the other characters get to point and laugh, and promptly lead the hunting of all dragons and other intrisically magic creatures to their extinction.

[Kinslayer]

I agree with you, KTheorem, the only thing preventing stacked bags is an artificial attempt to prevent a perceived player abuse.  

Instead of worrying about the nature of the storage space itself, consider the bags to simply be portals to that space.

If the cosmological assumption is that a portal directly links both sides without any intervening distance (which makes for a nice "default setting" as it doesn't require further explanation), then you can stack an infinite number of bags within one another without any difficulties.  

If instead, the cosmological assumption is that there must be a linking dimensional space (astral, ether, et al.), then at most the portals of the bags' openings would be inoperable while stacked--if and only if--the intervening dimension could not be accessed from within the bags' storage spaces except via their own portal opening. That is, you could still stack bags freely, but you would have to un-nest the bags to get at the desired object rather than just sticking your hand through a series of portals while still inside one another.  If this were the case, and the intervening dimension wasn't accessible from secondary portals within the storage dimension, there still wouldn't be an explosion, rift, or anything else catastrophic.  At most, they just wouldn't work--for purposes of taking something out or putting something in--while inside another bag. In no way would the nesting interfere with pre-extant storage.

Turning a bag inside out would then mean that either the contents would be dumped &/or the portal would be violated and made non-operational.  Unless there is an inherent explosion when a gate is shut down, or other catastrophic event, then it would simply stop operating at most--with or instead of the contents being dropped onto the ground.  

It should not be possible to completely stuff a bag of holding into itself, to make it disappear or whatever.  Since there would have to be some fabric still in the dimension of the holder to anchor and interact, it couldn't be completely dispersed into itself, no matter how hard you stuff or how fast your hands are moving.

[Kinslayer]

If the bags access the same sub-dimensional space (but still separate, unless you want to deal with Hackmaster's Bag World potential messes) the bags wouldn't work at all if nested.  There may theoretically be some local ripping of space-time if attempted.